DB's Deputy Commissioner (North) Moshiur Rahman confirmed the development on Wednesday.
But the brothers left Bangladesh for Thailand by an air ambulance less than a week later on May 25.
The charges also include firing a gun in an attempted murder and forcing Haider and Feroz into signing documents.
NBL has denied the charges. It levelled countercharges against Exim Bank, saying one of the Exim directors had taken loans from NBL and tried to borrow more through illegal means. The case against the Sikder brothers aims to belittle them, it added.
The two brothers later left Dhaka’s Shahjalal International Airport for Bangkok on May 25 by an air ambulance of R&R Aviation, a company owned by Sikder Group.
Both Ron, 47, and Dipu, 53, have US passports, a source at the airport law enforcement, told bdnews24.com.
The directors of R&R Aviation had travelled to Bangkok by the company’s aircraft several times earlier, he added.